Dutch FA president Michel Van Praag became the first official candidate but others could follow.
Angel Maria Villar of Spain, UEFA's senior vice president who will present the European Championship trophy on July 10th, and Slovenian football chief Aleksander Ceferin are also considered probable contenders.
Uefa's executive decided at a meeting in Basel on Wednesday — where Liverpool lost to Sevilla in the Europa League final — to hold the election in Athens in September rather than rush into a vote before the European Championship finals.
Platini is banned from any official capacity at Euro 2016 because of the four-year ban imposed over a suspect $2 million payment he received from Fifa in 2011.
The Frenchman announced he would quit on May 9th after losing an appeal at the Court of Arbitration for Sport.
Platini said in a statement released on Wednesday that he wanted to “formally resign” before Uefa's 55 national associations at the Athens congress in September when his successor is chosen.
“I want to leave by telling them, face to face, that I never cheated on their trust, nor failed in my duty and my values,” the former French football legend said in the statement.
Uefa's acting general secretary Theodore Theodoridis said that because of his Fifa suspension, Platini could be barred from any official function at Euro 2016, to be held in his native France from June 10th to July 10th.
Theodoridis said Uefa would have to check with Fifa on Platini's status.
Asked if Uefa could invite Platini to the tournament, Theodoridis responded: “I never said we're inviting or not inviting (him). But we have to clarify what we can do and what we cannot do. Any decision will follow, and it's not mine.”
Candidates will have until July 20th to put themselves forward for the Uefa presidency.
On top of Van Praag, Villar and Ceferin, Portugal's football association chief Fernando Gomes is also a possible candidate.
Villar, a former Athletic Bilbao player turned lawyer, has taken a prominent role in Uefa since Platini's suspension.
But he was warned and fined $25,000 by Fifa in November for his failure to cooperate with an inquiry into the bidding for the 2018 World Cup awarded to Russia and 2022 tournament to be held in Qatar.
Van Praag, a long-time president of the Royal Dutch Football Federation, stood against Sepp Blatter for the Fifa presidency in May last year but withdrew before voting started.
He said that if elected he would complete the two and half years left in Platini's term before handing over to a new president.
The 68-year-old Van Praag said he “wanted to steer Uefa into calmer waters… and pave the way for a new president”.